## Probabilistic Analyses and Fragility Curves

Fragility curves are cumulative distribution functions, which are used to describe the relationship between the acting loads and the probability of failure. The simplest way for deriving fragility curves is the empirical compilation of fragility curves based on damage assessment and engineering knowledge. A more precise prediction can be obtained with fragility curves based on experimental investigations or simulations. A typical example for a traditional simulation approach is the application of Monte-Carlo simulations, which consider both the stochastic characteristic of the seismic input and the variation of the resistance in terms of distribution functions or random fields.

A reduction of the computational time can be achieved by using „Response surface models“ (RSM - „meta-model“ ), which can be developed for each level of loading based on the principals of „Design of experiments“ (DOE). The response surface models deliver a mathematical description of the dependency between the significant input parameter and the structural response. These so-called meta-models enable an efficient evaluation of fragility curves. The probabilistic analysis is executed with the finite element software ANSYS, for which SDA-engineering GmbH developed special program modules using the APDL-programming language.

Thus SDA-engineering GmbH has the necessary competence to perform probabilistic analyzes for structures and components of customers and to design them for specified failure probabilities.